Question: Factor the following expression: $-5$ $x^2+$ $16$ $x+$ $16$
Explanation: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-5)}{(16)} &=& -80 \\ {a} + {b} &=& & & {16} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-80$ and add them together. Remember, since $-80$ is negative, one of the factors must be negative. The factors that add up to ${16}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-4}$ and ${b}$ is ${20}$ $ \begin{eqnarray} {ab} &=& ({-4})({20}) &=& -80 \\ {a} + {b} &=& {-4} + {20} &=& 16 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-5}x^2 {-4}x +{20}x +{16} $ Group the terms so that there is a common factor in each group: $ ({-5}x^2 {-4}x) + ({20}x +{16}) $ Factor out the common factors: $ x(-5x - 4) - 4(-5x - 4) $ Notice how $(-5x - 4)$ has become a common factor. Factor this out to find the answer. $(-5x - 4)(x - 4)$